Let and . What is the derivative of evaluated at…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let

f(t)=t^{2}

and

\mathbf r(t)=\langle\sin t, e^{t}\rangle

. What is the derivative of

f(t)\,\mathbf r(t)

evaluated at

t=1

? (a)

\big\langle \sin 1+2\cos 1,\;3e\big\rangle

(b)

\big\langle 2\sin 1,\;2e\big\rangle

(c)

\big\langle 2\sin 1+\cos 1,\;3e\big\rangle

(d)

\big\langle 2\sin 1+\cos 1,\;2e\big\rangle